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13.2. Calculating Stocking Ratio

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Author : David Bogert

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13 minutes

This is a very long and boring discussion of the very charged and opinionated topic of proper stocking of the aquarium. This article tackles the problem from a scientific viewpoint. This is very long winded discussion only for real nerds, like the author.

The Science

Note that there is some science here. And the science says that VERY VERY HEAVY stocking of aquarium tropical fish is quite healthy and does little harm to the fish.

Universities that raise zebrafish for research use a figure of five to fifteen zebrafish per liter as the optimum stocking. That is 1,895 to 5,685 one-inch (2.5cm) zebrafish per 100 gallons (378.5 liter), two to six times the stocking level of my “heavy” level. Consider that these universities need to keep these fish healthy to do their research. So they have done a lot of research which shows their stocking to be reasonably sound for fish health.

Hypsophrys Nicaraguensis
Hypsophrys Nicaraguensis

These data suggest that using stocking densities as high as 12 fish/L (46 per gallon) does not hurt performance, when measured by reproductive performance.

“The Effect of Stocking Densities on Reproductive Performance in Laboratory Zebrafish (Danio rerio)”, Castranova et. al., 2011:

It is concluded that adult laboratory zebrafish had a preference for a transparent or black background aquarium, at several 10 individuals per 2 L (20 per gallon) of available water volume, to express their normal behavior and avoid increased cortisol stress reaction.

“Husbandry of Zebrafish, Danio rerio, and the Cortisol Stress Response”, Pavlidis et. al. 2012:
Peacock Dragonblood
Peacock Dragonblood

The result of this study suggests that the stocking density of zebrafish could be 15 fish per 2 litres (29 per gallon) of water in a laboratory system with aeration.

“Effects of Stocking Density on Growth of Zebrafish”, Rabbane e. al.,  2016:

Comment from Shea

I just wanted to jump in as a zebrafish/zebra danio researcher to add some more specifics onto how heavy we’re able to stock our fish.

It’s not uncommon for us to stock 200+ adult zebrafish in 15 gallon (56.78 liter) (13 per gallon (3,79 liter)), bare bottom tanks. Our fish turn out fine morphologically/genetically, and are healthy for many years (healthy meaning able to spawn 50+ viable embryos. Some of our best breeders are 5+ years old).

The one caveat to this is that we house our fish in expensive commercial systems designed to maintain precise water parameters. These systems are also equipped with massive 25 gallon (94,6 liter) fluidised K1 sumps.

While obviously not representative of any home aquarium… The point I’m trying to make is that good biofiltration allows you to “get away” with a lot.

Aquaculture operations raising food fish like tilapia for consumption can run a very high stocking. And aquaculture operations run on very thin margins which will be negatively impacted by any fish death.

A quote is useful:

How many tilapia per gallon (3,79 liter)?

The consensus is that a pound (454 gram) of tilapia will need 3 gallons (11,4 liter) of water. A full-grown tilapia will weigh approximately 1 pound (454 gram) although they can grow larger.

This is one pound (454 gram) of fish for every three gallons (11,4 liter) of water or 33 pounds (14.982 gram) per 100 gallons (378.5 liter). The heaviest level shown in the charts below is for stocking 6.1 pounds (2.769 gram) of fish for every 100 gallons (378.5 liter). So obviously even the heaviest aquarium loading here is well below the level where fish health becomes a concern.

Aulonocara baenschi Sunshine Peacock
Aulonocara baenschi Sunshine Peacock

One Inch of Fish for Every Gallon of Water

The basic stocking “rule” (actually simply an OPINION) that has prevailed forever is “one inch of fish for every gallon of water” (one centimeter of fish for every liter of water). This is extremely inaccurate. It is the volume and weight of a fish, not its length, which is important.

Using the metabolic weights of the fish (calculated elsewhere), the one inch per gallon rule in a 100 gallon aquarium (100 inches of fish) will give:

  • one inch fish – 100×1 gram = 100 grams (light stocking)
  • two inch fish – 50×7 grams = 350 grams (moderate stocking)
  • four inch fish – 25×47 grams = 1,175 grams (heavy stocking)
  • eight inch fish – 13×167 grams = 2,171 grams (VERY heavy stocking)

Using the metabolic weights of the fish (calculated elsewhere), the one centimeter per liter rule in a 400 liter aquarium (400 centimeter of fish) will give:

  • two and half centimeter fish – 160×1 gram = 160 grams (light stocking)
  • five centimeter fish – 80×7 grams = 560 grams (moderate stocking)
  • ten centimeter fish – 40×47 grams = 1,880 grams (heavy stocking)
  • twenty centimeter fish – 20×167 grams = 3,340 grams (VERY heavy stocking)

This illustrates how inaccurate these “rules” are. The number of grams should be equal in my OPINION. But for small one to two inch (2.5 – 5cm) fish and beginners this is a good rule. It rapidly breaks down above 2 inches (5 cm). Beginners to the hobby and those that have new aquariums with new filters should not be doing any heavy stocking.

Aulonocara Turkis
Aulonocara Turkis

Rachel O’Leary Methodology

Rachel O’Leary (great YouTube channel) looks at each fish and calculates its “volume” in “cubic inches” (length multiplied by height multiplied by width).

Inch per gallon, fact or fiction

An “average” fish will weigh ten grams for each calculated “cubic inch”. So

  • a “normal fish” a five-inch peacock (including tail) is 5 inches by 1.5 inches tall by half an inch wide gives 5×1.5×0.5=3.75 so 3.75x 10=38 grams.
  • A five-inch discus (including tail) which is 3.5 inches high and 3/8ths of an inch wide is 5×3.5×0.375=6.6 so 6.6×10=66 grams.
  • A five inch fancy goldfish is 5×1.6×1.6=12.8 so 12.8×10=128 grams.

This “rule” is surprisingly accurate. Rachel O’Leary then uses an OPINION of recommended stocking being equal to one “cubic inch” or ten grams of this “volume” of fish for every ten gallons (37.85 liter), which works out to ten “cubic inches” or 100 grams to a 100-gallon (378.5 liter) tank.

This is a great method for very accurately determining the filtration requirements and the true stocking ratio. Note this is roughly 5% of the “heavy” stocking of the author’s OPINION below. But Rachel breeds fish. Breeding typically requires very low stocking.

Note also that I put the “volume” in quotes as the “true volume” of the actual fish is very very roughly 61% of the volume calculated by Rachel’s methodology.

Incredibly Heavy Stocking of an Aquarium
Incredibly Heavy Stocking of an Aquarium

Calculating Stocking Ratio in Depth

The best way to look at stocking is by poundage. If you can imagine all the fish in an aquarium in a pile in your hand. Ask yourself how much does that handful of fish weigh? Compare the pile to a pound of hamburger in your mind.

One then has to ask, “how active is my fish?” Small fish constantly swim around the tank while large fish tend to “hang out” without swimming. This metabolism factor is exceptionally large, a TYPICAL small one-inch (2,54 cm) fish will burn, pound for pound, roughly five times the calories of a TYPICAL large ten-inch (25,4 cm) fish.

Research data on a lot of fish says there is a sharp decrease in metabolism as one increases from six to nine inches (15,2 to 22.9 cm) in total length (body plus tail). Note this is a VERY VERY rough generalization with a huge number of exceptions.

Heavily Stocked Aquarium
Heavily Stocked Aquarium

To calculate the “metabolic weight” of a fish, a scientific article was required. In the paper “Length-weight Relationship of Nigerian Freshwater Fishes”, Richard King, 1996, gave the weight factors for 73 tropical freshwater fish populations ranging in length from 1.5 cm to 22.5 cm. He defined the weight of the fish by the equation W = A x LB where A ranges from 0.003 to 0.6 and B ranges from 2 to 5. The mean values for A were very roughly about 0.02 and the mean values for B were very roughly about 3, or W = 0.02 L³ . But there was a HUGE, and I must emphasize HUGE, amount of variability.

This formula, W= 0.02 L³, is accurate for a tilapia per the literature. A ten centimeter (four inch) tilapia is thus 21 grams.

Placidochromis sp. Phenochilus Tanzania Star Sapphire
Placidochromis sp. Phenochilus – Tanzania Star Sapphire

For trout, per the literature, the formula becomes:

W = 0.036 L²∙⁷

A ten centimeter (four inch) trout is thus 18 grams. This reflects the narrow streamlined shape of a trout.

For a catfish, per the literature, the equation becomes:

W = 0.0127 L³∙²⁸

A ten centimeter (four inch) catfish is thus 24 grams. This reflects the fat wide body of a catfish.

Complicated enough for you? Note this range of 18 to 24 grams is MUCH less than intuition says it should be.

Another factor that then needs to be added in is a “metabolism factor”. Smaller fish move much faster on average than a larger fish. So the weight needs to be changed to account for this.

Aulonocara walteri
Aulonocara walteri

From experience, I know a 100-gallon (378.5 liter) aquarium can hold about 50 four inch (10 cm) (total length) mbuna (50 x 37.8 = 1,890 grams metabolic weight) with VERY heavy stocking and VERY heavy filtration. The length-weight-metabolism factors of the Nigerian study were then melded with the mbuna stocking numbers and the following chart was the result:

Total length of fishActual weight in grams“Metabolic” weight in grams = x1780/x
1in 2,5cm0,3211890
2in 5cm2,56,76280
3in 7,6cm8,8519,597
4in 10cm2137,850
5in 12,7cm4157,433
6in 15,3cm70,570,527
8in 20,3cm16716711
10in 25,4cm3283286
12in 30cm5815813
Calculations for the number of fish for very heavy stocking in a 100 gallon (378,5 liter) aquarium
Weight and Stocking Calculations

The “actual weight” was derived from the Nigerian study equation where W = 0.02 L³.  The 1,890 number was obtained by multiplying 37.8 grams (weight of a four-inch (10 cm) fish per the study) by 50 four-inch fish (37.8 x 50 = 1,890).

One of my readers surveyed the aquarium literature and found that:

  • female guppy with a Total Length of 4.5 cm (1.77 inches) weighs 1.4 grams on average
  • platy-Xiphophorus maculatus with a Total Length of 4.8 cm (1.9 inches) is 1.8 grams average
  • Danio rerio of 1-year-old with a Total Length of 4.5 cm (1.77 inches) is 0.67 grams
  • 19 weeks young tiger barbs (Puntigrus tetrazona) with a average Total Length of 3.7 cm (1.46 inches) and weigh 0.85 grams
Cyrtocara moorii Albino Blue Dolphin
Cyrtocara moorii – Albino Blue Dolphin

This would say the weight numbers of King are higher for small fish than they should be. I revisited King to look at it. Another study that measured the length and weight of some juvenile Lake Malawi cichlids gave some more data (“Nutrition for Juvenile African Cichlids: the Effect of Varying Dietary Protein and Energy Levels on Growth Performance and Liver Condition” Royes, 2004). One reader (Jim O’Neill) did a rough measurement of the weight of some of his fish. Then there is the calculated weight per King. Putting it all together into a chart one gets:

Fish speciesLength in cmLength in inchesMeasured weight in gramsCalculated weight in grams
Neons2,881,20,60,48
Glowlight Tetra2,881,20,60,48
Cherry Barb3,31,30,80,72
Zebra Danio3,61,40,80,9
White Cloud3,61,40,80,9
Tiger Barb3,71,460,851,0
Mbuna3,81,50,51,1
Mbuna4,21,651,051,5
Guppy4,51,771,41,8
Zebra Danio4,51,770,671,8
Mbuna4,81,91,82,2
Platy4,81,91,82,2
Mbuna4,81,92,172,2
Red Eye Tetra52.02,72,6
Mbuna5,32,12,443,0
Mbuna62,363,184,3
Rams6,352,54,15,1
Rams7,12,85,97,2
Bueno Aires Tetra7,12,84,97,2
Goldfish11,44,535,630
Fish Length versus Weight

So King is a little higher. But I’m sticking with his numbers. It is important to emphasize that this is a GROSS APPROXIMATION ONLY. This number varies a HUGE amount depending on body shape. Smaller fish tend to be less “stocky” than larger fish in the aquarium versus in the wild. So it is not surprising they have smaller actual weights than an average of wild fish would say.

Dimidiochromis compressiceps Albino Malawi Eye Bitter
Dimidiochromis compressiceps Albino Malawi Eye Bitter

The last column in the “heavy stocking” chart above represents the number of fish that can go in an 100-gallon aquarium (378.5 liter) with very heavy stocking.  The numbers reflect the metabolism change that occurs at three to nine inches (7,6 to 22,9cm). We can then break out the “light stocking”, “Maximum recommended” (or “moderate”) and “heavy stocking.

Total length of fishLight stockingRecommended 100% level stockingHeavy stocking *
1in 2,5cm1816301890
2in 5cm2893280
3in 7,6cm103297
4in 10cm51750
5in 12,7cm31133
6in 15,3cm3927
8in 20,3cm1411
10in 25,4cm126
12in 30cm013
* ONLY with very heavy filtration
Number of fish for stocking in a 100 gallon or 378,54 liters aquarium

This chart is then divided by the appropriate number to get the stocking levels in the charts on the “13. Stocking” Page. These charts can be seen at this link:

13. Stocking

Now many will key in on the number “1,890” one-inch (2.5 cm) fish per 100 gallons (378.5 liter) and say “That is just ridiculous”. But the numbers are generally MUCH less than the stocking that several hundred university research centers use to stock zebrafish for genetic research.

Mixed Cichlid Aquarium
Mixed Cichlid Aquarium

Many hobbyists use a website called AqAdvisor to find out if they are properly stocked and filtered. AqAdvisor calculates roughly based on what is “moderate” stocking above for four inch (10 cm) fish. If you plug in the heavy stocking for a four inch fish above into the AqAdvisor calculator it will typically say “Your aquarium stocking level is 300%”. The “Your aquarium stocking level is 100%” recommended on AqAdvisor.com for a four-inch (10 cm) fish is roughly one-third the very heavy stocking level we calculate here-in, or a “moderate” level.

Note that the AqAdvisor.com website is just one person’s OPINION and the stocking calculator is NOT based on rational volume or weight considerations. For instance, the AqAdvisor calculator says 105 neons in a 100-gallon (378.5 liter) aquarium is the 100% stocking level (“Your aquarium stocking level is 100%” in AqAdvisor). This is a ridiculously low number of neons for a 100 gallon (378.5 liter). Any 100 gallon can easily stock 500 neons at “moderate” stocking and 1500 neons at “heavy” stocking.

The “Your aquarium stocking level is 100%” weight recommended on AqAdvisor.com for a one-inch (2,5 cm) fish is only 18% of the “Your aquarium stocking level is 100%” weight of four-inch (10 cm) fish on the same site. So this site is only OPINION which ignores volume and weight mathematical calculations. It appears the AqAdvisor.com site is based on the incredibly inaccurate one inch per gallon rule. (1cm per liter)

Heavy Neon Tetra Stocking
Heavy Neon Tetra Stocking

A 100 gallon (378.5 liter) aquarium can hold about 6 pounds (2,800 grams) of fish in heavy stocking,  2 pounds (900 grams) in moderate (“100% stocking level”) stocking, and 0.66 pounds (280 grams) in the light stocking. An eleven-inch (27,9 cm) Oscar will have a “metabolic” weight of 363, which means one can stock 2,800/363 or close to eight full-grown Oscars in a 100-gallon (378.5 liter) tank with VERY heavy stocking.

Note also that this is like every other aquarium variable. Namely “it depends”. If you have a superb large filter system, drip water changes, heavy aeration, your water parameters are perfect, etc. then it’s amazing how many fish you can stock.

Heavily Stocked Rift Valley Cichlid Aquarium
Heavily Stocked Rift Valley Cichlid Aquarium

Filtration and Stocking

Everyone in the hobby tends to make everything about the number of gallons in the aquarium. This is a mistake. It is possible to house very large fish in very small aquariums IF THE FILTRATION AND WATER CHANGES ARE SUFFICIENT!! I’ve seen a 50 gallon (189 liter) aquarium with two large (try one foot) (30 cm) Oscars which had been living there just fine for many years. There were two huge canister filters under the aquarium and the water was changed every three days by a drip water change system.

Remember the cardinal rule of filtration:

One Pound (454 gram) of Fish Needs 100 ft² (9,29 m²) Of Biomedia Surface Area

This amount of bio media give no nitrites, no ammonia, good water clarity, and good fish health.

There are ways to determine the amount of media and the amount of filtration needed for a given loading of fish. They can be found in the following link:

8.8. Sizing Filters and Media

Heavily Stocked Mixed Biotope Cichlid Aquarium
Heavily Stocked Mixed Biotope Cichlid Aquarium

Of course, there is always a downside to putting huge poundage of fish in a small aquarium. If the power goes out for more than an hour, fish in a heavily stocked aquarium will begin dying. I know, I lost a couple of thousand dollars of fish in a ten-hour power outage.

Anyone with heavily stocked aquariums must have a generator that can be set up in half an hour in the dark. Note that the cheap battery-operated air pumps lack the power to create bubbles with an air stone on the bottom of the aquarium. I find them of limited use.

Maylandia zebra Chilumba Maison Reef
Maylandia zebra – Chilumba Maison Reef

Filter Media

Now the common question here is “what do you mean by “good media”? Testing has shown some filter media to be much better than other filter media. This testing can be found in this article:

7.1.3. Filter Media Test

The green media below are what are considered “good media”:

Media“Efficiency” from two tests *“Effective” surface area ft²/ft³ ft²/ft³ from math“Effective” surface area m²/m³m²/m³ from math
Fluidized K1 medianot tested600na1980na
30 PPI foam1734040011221320
Pot scrubbers1428080924264
Static K1 media13260200858660
20 PPI foamnot tested220180726594
Aquarium gravel6120120396396
Blue Matala pads5100120330396
Eshoppe bioballs510060330198
¼ to ½ inch lava rocks36060198198
Matrix3603019899
Biohome ultimate2403013299
Ceramic rings24040132132
* average ammonia oxidizing that 15 cubic inches (245,81 cm³) of media accomplished over a 90-day period

Stocking in Greater Depth

Hopefully the following links can put some common sense into this subject:

13.1. Stocking Opinions

13.3. Lifespan of the Fish